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Abstract

Automation of alignment tasks can provide improved efficiency and greatly increase the flexibility of an optical system. Current optical systems with automated alignment capabilities are typically designed to include a dedicated wavefront sensor. Here, we demonstrate a self-aligning method for a reconfigurable system using only focal plane images. We define a two lens optical system with 8 degrees of freedom. Images are simulated given misalignment parameters using ZEMAX software. We perform a principal component analysis on the simulated data set to obtain Karhunen–Loève modes, which form the basis set whose weights are the system measurements. A model function, which maps the state to the measurement, is learned using nonlinear least-squares fitting and serves as the measurement function for the nonlinear estimator (extended and unscented Kalman filters) used to calculate control inputs to align the system. We present and discuss simulated and experimental results of the full system in operation.

Fig. 4. First 12 KL modes obtained from PCA decomposition with subframe 250×250 pixels. Each image is plotted under different intensity scale, and its corresponding eigenvalue is shown under the mode number in log scale.

Fig. 6. Residual error with modes 1–8 used in image reconstruction. Images are plotted under the same intensity scale. The reconstruction error decreases gradually as the number of modes used increases.

Fig. 9. RMS state residuals of IEFK and UKF in the simulation. Blue-diamond line and red-circle line represent IEKF and UKF estimation. Green-square line and the magenta-cross line represent the state residuals with full state feedback after the 25th step in IEKF and UKF, respectively.

Fig. 10. RMS standard deviation (STD) of state estimation using IEFK and UKF in the simulation. Blue-diamond line and red-circle line represent IEKF and UKF estimation. Green-square line and the magenta-cross line represent the STD of state estimate with full state feedback after the 25th step in IEKF and UKF, respectively.

Fig. 11. Experiment setup of optical model shown in Fig. 1. A collimated laser beam passes through a ND filter, two moving lenses A and B, and focuses on a CCD camera. The optical system after the ND filter is set up as the one simulated in ZEMAX.

Fig. 12. Residual error of the reconstruction of a single image acquired with the experimental setup shown in Fig. 11. The first eight KL modes derived in simulation are used. Images are plotted using the same intensity scale. As in simulation, the reconstruction error decreases gradually as the number of modes used increases.

Fig. 14. Experimental image before and after state feedback. The left image shows the 300×300 subframe before the correction, and the right image is the subframe after the correction. The intersection of the green lines represents the center of the camera.